{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 平面上的角度和三角学"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***2.3.1 角度到分量***\n",
    "1. 使用量角器(角度)和一把尺子(距离)组成的坐标称为极坐标\n",
    "2. sin 是垂直距离(y轴)(正弦)，cos是水平距离(x轴)(余弦)\n",
    "3. tan(正切) = $sin/cos$\n",
    "4. 有距离r,角度a。x = $r*cos(a)$ y = $r*sin(a)$\n",
    "5. cos($\\Theta$) = x / r , sin($\\Theta$) = y / r => tan($\\Theta$) = (y / r) / (x / r) = y / x\n",
    "6. 极坐标方便旋转，笛卡尔坐标方便平移"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***2.3.2 弧度***\n",
    "1. 1弧度 ≈ $57.296^°$  Π弧度 = $180^°$\n",
    "2. python是用弧度计算，所以在所以sin,cos,tan函数时，需要将角度转为弧度：$角度*(pi / 180)或(角度 * (pi / (360/2) ))$\n",
    "3. 弧度 = 度数 × (π / 180)\n",
    "4. 度数 = 弧度 × (180/π)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 接收极坐标，返回对应的笛卡尔坐标\n",
    "from math import sin,cos,tan\n",
    "def to_cartesian(polar_vector):\n",
    "    length,angle = polar_vector[0] , polar_vector[1]\n",
    "    return (length*cos(angle), length*sin(angle))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "# 勾股定理技术\n",
    "def length(v):\n",
    "    return sqrt(v[0]**2 + v[1]**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.993177550236464, 3.0090751157602416)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import pi\n",
    "angle = 37*pi/180\n",
    "to_cartesian((5,angle))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 接收笛卡尔坐标，返回对应的极坐标（第一个参数是距离，第二个参数是弧度(比如 pi/4)）\n",
    "from math import atan2\n",
    "def to_polar(vector):\n",
    "    x,y = vector[0], vector[1]\n",
    "    angle = atan2(y,x)\n",
    "    return (length(vector),angle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.605551275463989, 2.158798930342464)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_polar((-2,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.27：确认笛卡儿坐标(-1.34, 2.68)对应的向量的长度约为3。***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.9963310898497184\n"
     ]
    }
   ],
   "source": [
    "print(length((-1.34, 2.68)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.28：图2-45中是一条从x正半轴开始按逆时针方向旋转22°角的直线。根据图2-45，tan(22°)的近似值是多少？***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![jupyter](../images/img2-7.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "解：已知 y = 4,x = 10。有tan(22°) = sin(22°)/cos(22°)，sin(22°) = y / length, cos(22°) = x / length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4000002154065206\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "length = sqrt((10*10)+(4*4))\n",
    "sin1 = round(4/length , 6)\n",
    "cos1 = round(10/length , 6)\n",
    "tan1 = sin1 / cos1\n",
    "print(tan1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.29：转换问题的角度，假设我们知道了一个向量的长度和方向，想找到它的分量该如何做呢？一个长度为15的向量指向37°角，其x分量和y分量是多少？***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "利用公式：x = length * cos(a) , y = length * sin(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6457718232379019\n",
      "-0.6435381333569995\n",
      "0.7654140519453434\n"
     ]
    },
    {
     "data": {
      "image/png": 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SJ6fPAAD43XsvzLNnyZ6hMSmZoT7zSloGSktL0axZ1asX9Xo9Ly0kIqIqhIoKHI4eCvvx4wCANkuWwPumGxVOpR2SloGRI0di5syZaNOmDbp06YLdu3dj3rx5GD9+vJTTEhGRCynLy8Phi3caBIBOu3bWa1uArp2kHzr0/vvvY/To0ZgwYQI6d+6MF198EU899RSmT58u5bREROQiTn/+hVgE/Ebf77y3AIuA7CRdGfDx8cH8+fOveCkhERFpk1BRgazbh6C8oAAA0Pbzz+DVt6/CqbSL9yYgIiJZleXm4vDQO8QxtwWUx1sYExGRbE5/9plYBK4bM4bbAirBlQEiIpKcUFGBrKjBKC8sBAC0/fILePXurXAqqsQyQEREkirLycHhO+4Ux51270IzT08FE9HluE1ARESSKfr0U7EIXPfgA85tARYB1eHKABERNTrB4UDm4NvgOHUKANA25Ut43XCDwqnoSlgGiIioURn+/huHe/YSx9wWUD9uExARUaM58+mnCH/7HQBAi5iHuC3gIrgyQERE10xwOHBo4C1wnDkDAGj9+Wfw5YcIuQyuDBAR0TWxHcnGgS5dxSJwaMZ0ePbsqWwoqheWASIiarCi5GQcGT4cANDi4YfRfu8fEFRwC2WqH24TEBFRvQkOBw4NGAjH2bMAgLBlS+HZsyfsdruywahBWAaIiKhebEeO4MjwEeK40+970MxoVDARXStuExARUZ2d+vhjsQi0GPeo82oBFgGXx5UBIiK6KsHhQGa//qiwWgEAYV8tg2ePHgqnosbCMkBERLWyHT6MIyPuEsfcFmh6uE1ARERXdOrDj8Qi4B8by22BJoorA0REVI1QXo7Mm25GRUkJACDs6//Bs1s3hVORVFgGiIioCltWFo7cNVIcd/rjdzRzd1cwEUmN2wRERCQ6tXChWAT8H3vMuS3AItDkcWWAiIgglJfjYN8bIZw/DwAI+/preHbrqnAqkgvLABGRxl3IzET23aPEMbcFtIfbBEREGvb3f/4jFgH/uPHcFtAoSctAWFgYdDpdtV8TJ06UcloiIroKwW7HgR49cer9BQCAsG++QeDkyQqnIqVIuk2Qnp4Oh8Mhjv/8809ER0djzJgxUk5LRES1uHAwE9mj/tkWiPzjd+i4GqBpkpaBli1bVhnPmTMH7dq1w6BBg2o832azwWaziWPrxY+9tNvtit0JSxAE8auSd+OqnJsZmEFNOZjB9TIUffABziz8EABwXVwcAuInodz5G2XNISVmqJqhLnRC5audxMrKymA2m5GQkIBp06bVeE5iYiKSkpKqHU9JSYGXl5fUEWsUFxeHoqIimEwmJCcnK5KBiOiaORzo8Opr0F1crc15/jnYWrdWOBRJqbS0FDExMbBYLPD19a31XNnKwP/+9z/ExMQgNzcXZrO5xnNqWhkIDQ1FQUEBTCaTHDGrCQsLQ35+PsxmM44ePapIBsDZ8FJTUxEdHQ2DwcAMGs+glhzM4BoZbAczkTd6tDhut2sndBLlVPtjoaUMVqsVAQEBdSoDsl1amJycjGHDhl2xCACA0WiEsYbPvDYYDIo9mDqdTvyq5BN/JSUfC2ZQXwa15GAG9Wb4+733cOqDhQAA01NPodUL8YrkUILWM9RnXlnKQE5ODjZs2IDly5fLMR0RkeZVXi2AigoAQPiK5fDo3FnZUKRaspSBxYsXo1WrVhgxYoQc0xERadqFAweQfc+9zoFej8g9uyXbFqCmQfIPHaqoqMDixYsRGxsLNzd+4CERkZSK3ntfLAIBE55B531/sgjQVUn+6rxhwwbk5uZi/PjxUk9FRKRZgt2OjlNewpmL4/BVK+HRqZOimch1SF4Ghg4dCpkuWCAi0qQLf/2F7Pvudw7c3BC5exdXA6heeG8CIiIXVvjOPLEIFN1+O9qzCFADcBOfiMgFCWVlONC9hzgO/fYbZGZlKZiIXBlXBoiIXMz5ffvEIqBzd0fk3j9g7NhR4VTkylgGiIhcSOHbb+Po/c5PEwx49lnnTYa4LUDXiNsEREQuoKKsDAcv2RYI/24VPLgaQI2EKwNERCp3fu+fYhHQeXoi8s+9LALUqFgGiIhU7OTct3B0zBgAQMtJzzsvG+QHuFEj498oIiIVunxbIOL772Ds0EHBRNSUcWWAiEhlzu/dKxaBZt7eiPxzL4sASYplgIhIRU7OeRNHx4wFALSMj0ennRncFiDJ8W8YEZEKVNhsONijpziO+PEHGNu1Uy4QaQpXBoiIFHb+jz/EItDM19e5LcAiQDJiGSAiUtCJWbNwdOwDAICW/y8BnXb8xm0Bkh3/xhERKaDatsDqH2GMiFAuEGkaVwaIiGR2fs8esQjo/fwQue9PFgFSFMsAEZGMTkyfgaMPPgQAaPXi/0PH37ZDp9crnIq0jtsEREQyqLhwAQd79hLHEatXwxgRrmAion9wZYCISGKlu3eLRUDv739xW4BFgNSDZYCISEIn3piOnIdiAACtJk9Gx22/cFuAVIfbBEREEqi2LbBmNYzhXA0gdeLKABFRIyvddcm2QMsA57YAiwCpmORl4Pjx43jkkUdgMpng5eWFnj17YufOnVJPS0SkiIKkJOTEXNwWmDIFHbds4bYAqZ6k2wRnzpzBgAEDMHjwYKxZswatWrXC4cOHcd1110k5LRGR7HRlZcjq1l0ct1u3Fu5t2yqYiKjuJC0Db775JkJDQ7F48WLxWFhYmJRTEhHJ7vyuXejw6msAALfAQLTf+DN0zbgLS65D0jLw3Xff4Y477sCYMWOQlpaG1q1bY8KECXjyySdrPN9ms8Fms4ljq9UKALDb7bDb7VJGvSJBEMSvSmUAIM7NDMygphzMABQmvQHrN98AAFq8+P9gio1FucMBOByy5lD6cVBTDmaomqEudELlq50EPDw8AAAJCQkYM2YMduzYgfj4eHz00UcYN25ctfMTExORlJRU7XhKSgq8vLykilmruLg4FBUVwWQyITk5WZEMRKQ+urIycTUAALL/PRl2k0nBRERVlZaWIiYmBhaLBb6+vrWeK2kZcHd3R58+fbBt2zbx2PPPP4/09HT8+uuv1c6vaWUgNDQUBQUFMCn0jywsLAz5+fkwm804evSoIhkAZ8NLTU1FdHQ0DAYDM2g8g1pyaDXD+YwMHH98PADALTgY5u+/w4afftLc46DWHMzgZLVaERAQUKcyIOk2QXBwMK6//voqxzp37oxvv/22xvONRiOMRmO14waDQbEHU6fTiV+V/AdWScnHghnUl0EtObSUIf+VV2D5xvkcFjhtGvzHPSoux2rpcXCFHFrPUJ95JS0DAwYMwMGDB6scy8zMRFu+w5aIXExFaSkO3tBbHLdLXQ/30FAFExE1Hknf7vrCCy9g+/btmDVrFrKyspCSkoJFixZh4sSJUk5LRNSoSnbsEIuAwWxG5F/7WASoSZG0DPTt2xcrVqzA0qVL0bVrV0yfPh3z58/Hww8/LOW0RESNJn/ay8gdFwsACHzlFbT/+SdeNkhNjuT3Jrjrrrtw1113ST0NEVGjqigpwcHefcRxuw2pcA8JUTARkXRYb4mILlOy/TexCBhCQ53bAiwC1ITxroVERJfIn/ISLKtWAQACX3sV/hfvM0DUlLEMEBEBcJwrQWafS7cFNsA9pLWCiYjkw20CItK8ku3bxSLg3rbtxW0BFgHSDq4MEJGmHf/3v2H97nsAQFBiIlo8+IDCiYjkxzJARJp0+bZA+582wNCaqwGkTdwmICLNKdm27Z9tgYgIRO7/i0WANI0rA0SkKcdfnAzrDz8AAILeSEKLsWMVTkSkPJYBItIEx7lzyOzTVxy3//knGMxmBRMRqQe3CYioyTv3yy9iETB2aO/cFmARIBJxZYCImrTjCQmwrl4DAAia/gZajBmjcCIi9WEZIKImyVFcjMy+N4rj9ht/hiE4WMFEROrFbQIianLObdkqFgFjx47ObQEWAaIr4soAETUpxybFo3jdOgBA8MwZuO7++xVORKR+LANE1CQ4iouR1X+AOG6/aSMMQUEKJiJyHdwmICKX53XwILIvFgFj587ObQEWAaI648oAEbm0ghdeQMiGnwAAwbNm4br77lU4EZHrYRkgIpfksFqReeNN4jhsQyo8Q0IUTETkurhNQEQu51xamlgEjNdfj8w5s+EWGKhwKiLXxTJARC4l79lnkffU0wCA4DmzEfrVMkCnUzgVkWvjNgERuQSHxYLMm24Wx+3T0mAIbAW73a5gKqKmgSsDRKR6xRs3ikXAo1s359UCga0UTkXUdHBlgIhULe+ZCTi3cSMAwDz3TfjdfbfCiYiaHklXBhITE6HT6ar8CuK1v0RUB46zZ7E/srNYBNpvTmMRIJKI5CsDXbp0wYYNG8SxXq+XekoicnHFP/+MYxMmAgA8enRH2LJl0PFNgkSSkbwMuLm51Xk1wGazwWaziWOr1QoAsNvtir1JSBAE8auSb1SqnJsZmEFNOaTIkD9hIkq3bAEABM6ZDZ8RI1BeXi5rhvpiBnXlYIaqGepCJ1S+2kkgMTERb731Fvz8/GA0GnHTTTdh1qxZiIiIuOL5SUlJ1Y6npKTAy8tLqpi1iouLQ1FREUwmE5KTkxXJQKQFzUpK0P6N6eL48Csvw+Hjo2AiItdWWlqKmJgYWCwW+Pr61nqupGVgzZo1KC0tRceOHXHy5EnMmDEDBw4cwL59+2AymaqdX9PKQGhoKAoKCmo8Xw5hYWHIz8+H2WzG0aNHFckAOBteamoqoqOjYTAYmEHjGdSSo7EynPt5I05MmgQA8OjZE60/W1LnbYGm9Di4ega15GAGJ6vVioCAgDqVAUm3CYYNGyb+727duqFfv35o164dlixZgoSEhGrnG41GGI3GascNBoNiD2blE5JOp1P0H1glJR8LZlBfBrXkaGgGQRCQ9+S/ULJ1KwDA/Pbb8LtrhKwZGhMzqCuH1jPUZ15ZLy309vZGt27dcOjQITmnJSIVKj9zBof69RfHHbZugVtAgIKJiLRL1g8dstls2L9/P4KDg+WclohUxpqaKhYBzz69Ebn/LxYBIgVJujLw4osvYuTIkWjTpg0KCwsxY8YMWK1WxMbGSjktEamUIAjIi3sCJdu2AQBaz3sHvsOHK5yKiCQtA8eOHcNDDz2EU6dOoWXLlrj55puxfft2tG3bVsppiUiFqm0L/LIVbgq9MZiIqpK0DCxbtkzKP56IXIR13Xocv3i1gNeNN6LNkk/5IUJEKsJ7ExCRZARBQO748Sj9dTsAoPX8/4PvnXcqnIqILscyQESSKD99Gof6DxDHHbb9Ajd/fwUTEdGV8BbGRNTorGvXiUXAq9/NzqsFWASIVIsrA0TUaARBQO64WJSmpwMAWr/7LnzvGKpwKiK6GpYBImoU5UVFODRgoDju8Os2uLVooWAiIqorbhMQ0TUrXrtOLALe/fs7twVYBIhcBlcGiKjBBEFAyIcf4mT2UQBA6/fehe9QbgsQuRqWASJqkPJTp3B44C2ovLk4twWIXBe3CYio3iw//ohDA28BAJR07Ih2f/zOIkDkwrgyQER1JggCch6Kwfk9ewAAQfPnY7PtAnrw0wSJXBrLABHVSfnff+PQLbeK4w6/boPQvDmwerWCqYioMXCbgIiuyvL9D2IR8L71FnQ+sJ/bAkRNCFcGiOiKBEFAzoMP4fzvvwMAQj74D3xuu03hVETU2FgGiKhG9sJCZN06SBx33P4r9Nddp1wgIpIMtwmIqBrL99+LRaB5VBQ6H9jPIkDUhHFlgIhEgiDg6NgHcGHvXgBAyMIP4DN4sMKpiEhqLANEBACwnyxE1qBLtgV+2w69n5+CiYhILtwmICJYVq0Si0Dz2293bguwCBBpBlcGiDRMEAQcvX80Lvz1FwAg5MOF8ImKUjYUEcmOZYBIo+wnTyJrUJQ47rjjN+h9fZULRESK4TYBkQadXb5CLAI+0UOc2wIsAkSaJVsZmD17NnQ6HeLj4+WakoguIwgCjtxzLwqmTQMAhC76CCHvv69wKiJSmizbBOnp6Vi0aBG6d+8ux3REVAP7iRPIivrnMkFuCxBRJclXBs6dO4eHH34YH3/8MVrws8yJFHH222/FIuBzxx3cFiCiKiRfGZg4cSJGjBiBIUOGYMaMGbWea7PZYLPZxLHVagUA2O122O12SXNeiSAI4lelMgAQ52YGZqhPDkEQkHff/SjLygIABC/8AN4DBzZadjU8FsygngxqycEMVTPUhU6ofLWTwLJlyzBz5kykp6fDw8MDUVFR6NmzJ+bPn1/j+YmJiUhKSqp2PCUlBV5eXlLFrFVcXByKiopgMpmQnJysSAaihnA7exYRs+eI46zERFR4eiiYiIjkVFpaipiYGFgsFvheZSVQspWBvLw8TJo0CevXr4eHR92egKZOnYqEhARxbLVaERoaisGDB8NkMkkVtVZGo1H8Onz4cEUyAM6Gl5qaiujoaBgMBmbQeIar5bAuX47Ci0Wg+Z13IuituWgvcwa5MIN6MqglBzM4Va6u14VkZWDnzp0oLCxE7969xWMOhwObN2/GggULYLPZoNfrq/weo9EovvheymAwKPZg6nQ68auS/8AqKflYMIP6MlyeQxAEHBk5EmVZhwEAoZ98guYDB8iaQSnMoJ4Masmh9Qz1mVeyMnD77bdj78WbnVR6/PHHERkZiSlTplQrAkR0bewFBcgafJs47piRDn3z5gomIiJXIVkZ8PHxQdeuXasc8/b2hslkqnaciK7Nmf/9Dydeex0A4DtiBFq/87bCiYjIlfDjiIlcmSAg5+5RsGdnAwDa/DcZ3v37KxyKiFyNrGVg06ZNck5H1KTZ8/PR8aWpqLx4qGNGBvTNvRXNRESuifcmIHJBZ5Z9hZw77gQA+Nx1l/NDhFgEiKiBuE1A5EIEQcCRO4ehLCcHAJD35BMY/PzzCqciIlfHlQEiF1F27DgOdL5eLAIR23/F+fZSfHoAEWkNywCRCzizdCkODxkCAPAbdTc6H9iPZt7cFiCixsFtAiIVEyoqcPiOO2HPywMAtPn0U3jffJPCqYioqWEZIFKpsmPHcHhItDjutDODqwFEJAluExCp0OkvvxSLgN+993JbgIgkxZUBIhURKipwOHoo7MePAwDaLFkC75tuVDgVETV1LANEKlGWl4fD0UPFcaddO9FMoVt3E5G2cJuASAVOf/6FWAT8Rt/v3BZgESAimXBlgEhBQkUFsm4fgvKCAgBA288/g1ffvgqnIiKtYRkgUkhZbi4OD71DHHNbgIiUwm0CIgWc/uwzsQhcN2YMtwWISFFcGSCSkVBRgayowSgvLAQAtP3yC3j17q1wKiLSOpYBIpmU5eTg8MU7DQJAp9270MzTU8FERERO3CYgkkHRp5+KReC6Bx9wbguwCBCRSnBlgEhCgsOBQ4Oi4Dh1CgDQNuVLeN1wg8KpiIiqYhkgkogtOxtHhg0Xx9wWICK14jYBkQSKkv8rFoEWMQ9xW4CIVI0rA0SNSHA4cGjgLXCcOQMAaJuSAq8beimcioiodiwDRI3EdiQbR4Zfsi2wZzeaeXgomIiIqG64TUDUCIo++UQsAi0efti5LcAiQEQugisDRNdAcDhwqP8AOCwWAEDYsqXw7NlT2VBERPUk6crAwoUL0b17d/j6+sLX1xf9+vXDmjVrpJySSDZlR7JxoEtXsQh0+n0PiwARuSRJy0BISAjmzJmDjIwMZGRk4LbbbsOoUaOwb98+KaclklyLjZuQO2qU83+Pe9S5LWA0KpyKiKhhJN0mGDlyZJXxzJkzsXDhQmzfvh1dunSpdr7NZoPNZhPHVqsVAGC322G326WMekWCIIhflcoAQJybGZTNIDgcyL7lVrQsLgYAhHz5BTy6d1ckj9KPBTMwg1pzMEPVDHWhEypf7STmcDjw9ddfIzY2Frt378b1119f7ZzExEQkJSVVO56SkgIvhe7oFhcXh6KiIphMJiQnJyuSgdTB/WQhwubNE8eHZkyHYDAomIiI6MpKS0sRExMDi8UCX1/fWs+VvAzs3bsX/fr1w4ULF9C8eXOkpKRg+CWXX12qppWB0NBQFBQUwGQySRnzisLCwpCfnw+z2YyjR48qkgFwNrzU1FRER0fDoNALkJYznP74Y5x+730AgM/DD2Nn926KPg6Atv97MIM6M6glBzM4Wa1WBAQE1KkMSH41QadOnbBnzx6cPXsW3377LWJjY5GWllbjyoDRaISxhn1Xg8Gg2IOp0+nEr0r+A6uk5GOhxQxCeTkyb7oZFSUlAICwr/8Ht8hIYPVqVTwOgLb+ezCDa2RQSw6tZ6jPvJKXAXd3d7Rv3x4A0KdPH6Snp+Pdd9/FRx99JPXURNfElpWFI3f9876XTn/8jmbu7orvyRIRNTbZP3RIEIQqWwFEanRq4UKxCPg//rjzagF3d4VTERFJQ9KVgWnTpmHYsGEIDQ1FcXExli1bhk2bNmHt2rVSTkvUYEJ5OQ72vRHC+fMAgLCvv4Znt64KpyIikpakZeDkyZN49NFHUVBQAD8/P3Tv3h1r165FdHS0lNMSNciFzExk3z1KHFduCxARNXWSlgFeikeu4u///Aen3l8AAPCPG4/AyZMVTkREJB/em4A0TbDbcbB3HwhlZQCAsG++gWfX6h+IRUTUlLEMkGZdOJiJ7FH/bAtE/vE7dNwWICIN4i2MSZP+fn+BWARMTz6Jzgf2swgQkWZxZYA0RbDbcaDXDUB5OQAgfPm38KjhA7CIiLSEZYA048LBg8gedY845rYAEZETtwlIE/5+7z2xCJieeorbAkREl+DKADVpgt2OAz16AhUVAIDwFcvh0bmzsqGIiFSGZYCarAsHDiD7nnudA70ekXt2Q6eCG7gQEakNtwmoSSqcP18sAgETnkHnfX+yCBARXQFXBqhJEcrKcKB7D3EcvmolPDp1UjAREZH6sQxQk3Hhr7+Qfd/9zoHBDZG7dnE1gIioDrhNQE1C4TvzxCIQMGECOu/dyyJARFRHXBkgl1Z9W2AVPDp1VDAREZHr4coAuazz+/aJRUDn7o7IvX+wCBARNQDLALmkU/P+D0fvHw0ACHj2WeenCXJbgIioQbhNQC5FKCtDxykv4ezFcfh3q+DRkasBRETXgisD5DLO7/0Th3v3AQDoPD0Q+edeFgEiokbAMkAu4eSbc3F0zBgAwKmh0Wi3Ywd0blzYIiJqDHw2JVWrKCvDwUuuFghdsRyZmZkKJiIianq4MkCqdX7vXrEINPP2RuSfe2Fs317hVERETQ/LAKnSyTlv4uiYsQCAlvHx6LQzg9sCREQSkbQMzJ49G3379oWPjw9atWqFe+65BwcPHpRySnJxFTYb9kd2xulPPwUARPz4AwKefkrZUERETZykZSAtLQ0TJ07E9u3bkZqaivLycgwdOhQlJSVSTksu6vwff+Bgj54AgGa+vs5tgXbtlA1FRKQBkq67rl27tsp48eLFaNWqFXbu3Ilbb71VyqnJxZyYNQtnPvscANAyIQEB/3pS4URERNoh6yasxWIBAPj7+9f4fZvNBpvNJo6tVisAwG63w263Sx+wBoIgiF+VygBAnLupZaiw2XCkT19x3GbVKrhHhF9xjqb6OLhqDmZgBjXmYIaqGepCJ1S+2klMEASMGjUKZ86cwZYtW2o8JzExEUlJSdWOp6SkwMvLS+qINYqLi0NRURFMJhOSk5MVydBUeeTkos0HHwAAHF5eOPzqK0AzvqeViKgxlJaWIiYmBhaLBb6+vrWeK1sZmDhxIn788Uds3boVISEhNZ5T08pAaGgoCgoKYDKZ5IhZTVhYGPLz82E2m3H06FFFMgDOhpeamoro6GgYFPoM/sbM8Pes2bAsXQoAML0Qjxbjx8ueoaHUkEEtOZiBGdSYgxmcrFYrAgIC6lQGZNkmeO655/Ddd99h8+bNVywCAGA0GmE0GqsdNxgMij2YOp1O/KrkP7BKSj4WjZGh4sIFHOzZSxxHrF4NY0S4rBkaixoyqCUHMzCDGnNoPUN95pV0TVYQBDz77LNYvnw5fv75Z4SH1/9Jn5qO0t27xSKg9/dH5L4/G1QEiIiocUm6MjBx4kSkpKRg1apV8PHxwYkTJwAAfn5+8PT0lHJqUpkTb7yBMynObYFWkyfDFFe3bQEiIpKepGVg4cKFAICoqKgqxxcvXozHHntMyqlJJaptC6xZDSNXiIiIVEXSMiDTexNJpUp37UJOzMMAAH3LAHTYtAk6vV7hVEREdDlex0WSKEhMFItAqylT0HHLFhYBIiKV4p1fqFFVnD+Pg71uEMft1q2Fe9u2CiYiIqKr4coANZrSnTvFIuAWGIjIv/axCBARuQCWAWoUBa+9jpyHHwEABE6big5pm6DjpwkSEbkEbhPQNakoLcXBG3qL43br18G9TRsFExERUX3xRzdqsNL0dLEIuAUHO7cFWASIiFwOVwaoQfJfeQWWb74FAAROmwb/cY8qnIiIiBqKZYDqRVdWhqxu3cVxu9T1cA8NVTARERFdK5YBqrPz6Rno8OprAABD69Zol7qebxIkImoCWAaoTvKnvQzL8uUAgICpU9EydpzCiYiIqLGwDFCtKkpKcLB3H3F8ZMq/0T7mIQUTERFRY+MaL11RyfbfxCJgCA1Fu9/3oNzfX+FURETU2LgyQDXKn/ISLKtWAQACX3sV/jExsNvtCqciIiIpsAxQFY5zJcjs88+2QLsNG+Ae0lrBREREJDVuE5CoZPt2sQi4t23r/BAhFgEioiaPKwMEADj+73/D+t33AICgxES0ePABhRMREZFcWAY07vJtgfY/bYChNVcDiIi0hNsEGlaybds/2wIREYjc/xeLABGRBnFlQKOOvzgZ1h9+AAAEvZGEFmPHKpyIiIiUwjKgMY5z55DZp684bv/zTzCYzQomIiIipXGbQEPO/fKLWATc27dzbguwCBARaR5XBjTieEICrKvXAACCpr+BFmPGKJyIiIjUgmWgiXMUFyOz743iuP3Gn2EIDlYwERERqY2k2wSbN2/GyJEjYTabodPpsHLlSimno8uc27JVLALGTp2c2wIsAkREdBlJy0BJSQl69OiBBQsWSDkN1eDYpHjkPfkkACB45gxErFoJnU6ncCoiIlIjSbcJhg0bhmHDhtX5fJvNBpvNJo6tVisAwG63K3aTHEEQxK9K3qincu6rZXAUFyO7/wBxHJa6Hm5BQY2Sva4ZpMQM6srBDMygxhzMUDVDXeiEylc7iel0OqxYsQL33HPPFc9JTExEUlJSteMpKSnw8vKSMN2VxcXFoaioCCaTCcnJyYpkqCuvAwcRsngxAOCCORi5zz8PcDWAiEiTSktLERMTA4vFAl9f31rPVVUZqGllIDQ0FAUFBTCZTDKkrC4sLAz5+fkwm804evSoIhkAZ8NLTU1FdHQ0DAZDte8XxL+Akp9+AgC0mj4dvveMkj2DHJhBXTmYgRnUmIMZnKxWKwICAupUBlR1NYHRaITRaKx23GAwKPZgVu6z63Q6Rf+BVbr8sXBYrci88SZx3D5tEwyBgbJmUAIzqCsHMzCDGnNoPUN95uWHDrmw4k2bxCLg0aWL82oBiYsAERE1PapaGaC6y5v4LM5d3BYInjMb19Wy/UJERFQbScvAuXPnkJWVJY6zs7OxZ88e+Pv7o02bNlJO3WQ5LFZkDRwojtunpcEQ2ErBRERE5Ook3SbIyMhAr1690KtXLwBAQkICevXqhddee03KaZss7/37kX2xCHh063ZxW4BFgIiIro2kKwNRUVGQ6WKFJi//uefQelMaAMA890343X23womIiKip4HsGVM5x9iwyb+4njsN+/gmevNMgERE1Il5NoGLFP/8sFgFj927InDMbbi1bKpyKiIiaGpYBlcp96ikcmzARAGB+6y2EfvklP02QiIgkwW0ClSk/cwaH+vUXxx22bIZby5aKf944ERE1XVwZUJHin34Si4Bnr16I3P8XtwWIiEhyXBlQAUEQkPfkv1CydSsAwPz22/C7a4TCqYiISCtYBhRWbVtg6xa4BQQomIiIiLSG2wQKsq5f/8+2QJ/ezm0BFgEiIpIZVwYUIAgC8uLiULLtVwBA63nvwHf4cIVTERGRVrEMyKzatsAvW+FmMimYiIiItI7bBDKyrvtnW8Drxhud2wIsAkREpDCuDMhAEATkPj4epdu3AwBaz/8/+N55p8KpiIiInFgGJFZ++jQO9R8gjjts+wVu/v4KJiIiIqqK2wQSsq5dJxYBr343O7cFWASIiEhluDIgAUEQkDsuFqXp6QCA1u++C987hiqcioiIqGYsA42svKgIhwYMFMcdft0GtxYtFExERERUO24TNCLrmjViEfDu39+5LcAiQEREKseVgUYgCAJyHn0U5zN2AgBav/cufIdyW4CIiFwDy8A1Kj91CocG3iKOuS1ARESuhtsE18Dy449iEfAeOJDbAkRE5JK4MlADi8WC4uJihISEVPvesWPH0Lx5c5x9+hmc37MHABCy4H34DBkic0oiIqLGIcvKwAcffIDw8HB4eHigd+/e2LJlixzTNojFYsGdd96JQYMGIS8vr8r38vLyMGrQIBTc3E8sAh1+3cYiQERELk3yMvDVV18hPj4eL7/8Mnbv3o1bbrkFw4YNQ25urtRTN0hxcTEKCwtx5MgRREVFweFwAAAcDgdeH3wbvjC4AwD0N/ZF5wP7uS1AREQuT/IyMG/ePMTFxeGJJ55A586dMX/+fISGhmLhwoVST90gISEh2LRpEyIiInDkyBH8/fffAICyU6cw2c25q+KRlISOn32mZEwiIqJGoxMEQZDqDy8rK4OXlxe+/vpr3HvvveLxSZMmYc+ePUhLS6tyvs1mg81mE8dWqxWhoaEICgqCXq+XKmaNHA4H/v77b3FloBmAlm5ugL8/3AwGWbMAzssXbTYbjEYjdDqd7PMzg7oyqCUHMzCDGnMwg1NFRQUKCgpgsVjg6+tb67mSvoHw1KlTcDgcCAwMrHI8MDAQJ06cqHb+7NmzkZSUVO14TefKrQLAyfJyoLBQ6ShERESNSparCS5vRYIg1NiUpk6dioSEBHGsppUBANDr9WjZsqXsWQB1tExmUE8GteRgBmZQYw5mcKpcGagTQUI2m03Q6/XC8uXLqxx//vnnhVtvvfWqv99isQgAhFOnTkkVsUa5ublCRESEAEDQ6/VVvkZERAi5ubmy5hEEQSgrKxNWrlwplJWVyT43M6gvg1pyMAMzqDEHMzhVvoZaLJarnivpGwjd3d3Ru3dvpKamVjmempqK/v37Szl1gx07dgxRUVE4cuQIIiIi0LJlSwBAy5YtxTcVRkVF4dixYwonJSIiahySX02QkJCATz75BP/973+xf/9+vPDCC8jNzcXTTz8t9dQN4uPjg1atWiEiIgKbNm0StwT0er14lUGrVq3g4+OjcFIiIqLGIfl7Bh544AEUFRXhjTfeQEFBAbp27YrVq1ejbdu2Uk/dIH5+fli7dm2Nn0AYGhqKtLQ0+Pj4wM/PT6GEREREjUuWNxBOmDABEyZMkGOqRuHn53fFF/uaPqKYiIjIlfFGRURERBrHMkBERKRxLANEREQaxzJARESkcSwDREREGscyQEREpHEsA0RERBrHMkBERKRxLANEREQaxzJARESkcSwDREREGscyQEREpHEsA0RERBrHMkBERKRxLANEREQaxzJARESkcSwDREREGscyQEREpHEsA0RERBrHMkBERKRxLANEREQaxzJARESkcSwDREREGidpGZg5cyb69+8PLy8vXHfddVJORURERA0kaRkoKyvDmDFj8Mwzz0g5DREREV0DNyn/8KSkJADAp59+WqfzbTYbbDabOLZYLACA06dPN3q2unI4HOLXoqIixXLY7XaUlpaiqKgIBoOBGTSeQS05mIEZ1JiDGZyKi4sBAIIgXPVcSctAfc2ePVssEJfq2LGjAmmqOnHiBAICApSOQUREVC/FxcXw8/Or9RxVlYGpU6ciISFBHJ89exZt27ZFbm7uVf+PSMVqtSI0NBR5eXnw9fVVJINacjCDejKoJQczMIMaczCDkyAIKC4uhtlsvuq59S4DiYmJNf70fqn09HT06dOnvn80jEYjjEZjteN+fn6K/uUGAF9fX8UzqCUHM6gng1pyMAMzqDEHM6DOP0jXuww8++yzePDBB2s9JywsrL5/LBERESmk3mUgICCAe+dERERNiKTvGcjNzcXp06eRm5sLh8OBPXv2AADat2+P5s2bX/X3G41GvP766zVuHchFDRnUkoMZ1JNBLTmYgRnUmIMZ6k8n1OWagwZ67LHHsGTJkmrHN27ciKioKKmmJSIionqQtAwQERGR+vHeBERERBrHMkBERKRxLANEREQaxzJARESkcS5TBpS6HfIHH3yA8PBweHh4oHfv3tiyZYtscwPA5s2bMXLkSJjNZuh0OqxcuVLW+WfPno2+ffvCx8cHrVq1wj333IODBw/KmgEAFi5ciO7du4uf5tWvXz+sWbNG9hyXmj17NnQ6HeLj42WbMzExETqdrsqvoKAg2eavdPz4cTzyyCMwmUzw8vJCz549sXPnTlkzhIWFVXssdDodJk6cKFuG8vJyvPLKKwgPD4enpyciIiLwxhtvoKKiQrYMgPOz5+Pj49G2bVt4enqif//+SE9Pl2y+qz0vCYKAxMREmM1meHp6IioqCvv27ZM1w/Lly3HHHXcgICAAOp1OvLS9sdWWw263Y8qUKejWrRu8vb1hNpsxbtw45OfnS5LlWrhMGVDidshfffUV4uPj8fLLL2P37t245ZZbMGzYMOTm5sqWoaSkBD169MCCBQtkm/NSaWlpmDhxIrZv347U1FSUl5dj6NChKCkpkTVHSEgI5syZg4yMDGRkZOC2227DqFGjGv0Jpq7S09OxaNEidO/eXfa5u3TpgoKCAvHX3r17ZZ3/zJkzGDBgAAwGA9asWYO//voL77zzjqwlHXD+N7j0cUhNTQUAjBkzRrYMb775Jj788EMsWLAA+/fvx9y5c/HWW2/h/fffly0DADzxxBNITU3F559/jr1792Lo0KEYMmQIjh8/Lsl8V3temjt3LubNm4cFCxYgPT0dQUFBiI6OFu+iJ0eGkpISDBgwAHPmzGm0Oeubo7S0FLt27cKrr76KXbt2Yfny5cjMzMTdd98taaYGEVzM4sWLBT8/P1nmuvHGG4Wnn366yrHIyEjhpZdekmX+ywEQVqxYocjclQoLCwUAQlpamqI5BEEQWrRoIXzyySeyz1tcXCx06NBBSE1NFQYNGiRMmjRJtrlff/11oUePHrLNV5MpU6YIAwcOVDRDTSZNmiS0a9dOqKiokG3OESNGCOPHj69y7L777hMeeeQR2TKUlpYKer1e+OGHH6oc79Gjh/Dyyy9LPv/lz0sVFRVCUFCQMGfOHPHYhQsXBD8/P+HDDz+UJcOlsrOzBQDC7t27JZm7rjkq7dixQwAg5OTkSJ6nPlxmZUBuZWVl2LlzJ4YOHVrl+NChQ7Ft2zaFUinPYrEAAPz9/RXL4HA4sGzZMpSUlKBfv36yzz9x4kSMGDECQ4YMkX1uADh06BDMZjPCw8Px4IMP4siRI7LO/91336FPnz4YM2YMWrVqhV69euHjjz+WNcPlysrK8MUXX2D8+PHQ6XSyzTtw4ED89NNPyMzMBAD8/vvv2Lp1K4YPHy5bhvLycjgcDnh4eFQ57unpia1bt8qWo1J2djZOnDhR5bnTaDRi0KBBmn7urGSxWKDT6WRfSbsaVd3CWE1OnToFh8OBwMDAKscDAwNx4sQJhVIpSxAEJCQkYODAgejatavs8+/duxf9+vXDhQsX0Lx5c6xYsQLXX3+9rBmWLVuGXbt2SbofW5ubbroJn332GTp27IiTJ09ixowZ6N+/P/bt2weTySRLhiNHjmDhwoVISEjAtGnTsGPHDjz//PMwGo0YN26cLBkut3LlSpw9exaPPfaYrPNOmTIFFosFkZGR0Ov1cDgcmDlzJh566CHZMvj4+KBfv36YPn06OnfujMDAQCxduhS//fYbOnToIFuOSpXPjzU9d+bk5MieR00uXLiAl156CTExMYrfTfFyiq4M1PRmqMt/ZWRkKBmx2k8ZgiDI+pOHmjz77LP4448/sHTpUkXm79SpE/bs2YPt27fjmWeeQWxsLP766y/Z5s/Ly8OkSZPwxRdfVPspTC7Dhg3D/fffj27dumHIkCH48ccfAaDGj/2WSkVFBW644QbMmjULvXr1wlNPPYUnn3wSCxculC3D5ZKTkzFs2LA63be9MX311Vf44osvkJKSgl27dmHJkiV4++23Zf3vAQCff/45BEFA69atYTQa8d577yEmJgZ6vV7WHJfic2dVdrsdDz74ICoqKvDBBx8oHacaRVcG1Hw75ICAAOj1+mqrAIWFhdUarxY899xz+O6777B582aEhIQoksHd3R3t27cHAPTp0wfp6el499138dFHH8ky/86dO1FYWIjevXuLxxwOBzZv3owFCxbAZrPJ/uTr7e2Nbt264dChQ7LNGRwcXG1FpnPnzvj2229ly3CpnJwcbNiwAcuXL5d97smTJ+Oll14Sn8e6deuGnJwczJ49G7GxsbLlaNeuHdLS0lBSUgKr1Yrg4GA88MADCA8Ply1DpcqrW06cOIHg4GDxuFafOwFnERg7diyys7Px888/q25VAFC4DKj5dsju7u7o3bs3UlNTce+994rHU1NTMWrUKAWTyUsQBDz33HNYsWIFNm3apMiTy5UIggCbzSbbfLfffnu1d+4//vjjiIyMxJQpUxT5Kcxms2H//v245ZZbZJtzwIAB1S4vzczMRNu2bWXLcKnFixejVatWGDFihOxzl5aWolmzqguser1e9ksLK3l7e8Pb2xtnzpzBunXrMHfuXNkzhIeHIygoCKmpqejVqxcA53s60tLS8Oabb8qeR2mVReDQoUPYuHGjbNt59eUy7xm41tshN0RCQgIeffRR9OnTB/369cOiRYuQm5uLp59+WpL5anLu3DlkZWWJ4+zsbOzZswf+/v5o06aN5PNPnDgRKSkpWLVqFXx8fMSVEj8/P3h6eko+f6Vp06Zh2LBhCA0NRXFxMZYtW4ZNmzZh7dq1smXw8fGp9l4Jb29vmEwm2d5D8eKLL2LkyJFo06YNCgsLMWPGDFitVll/Cn3hhRfQv39/zJo1C2PHjsWOHTuwaNEiLFq0SLYMlSoqKrB48WLExsbCzU3+p7ORI0di5syZaNOmDbp06YLdu3dj3rx5GD9+vKw51q1bB0EQ0KlTJ2RlZWHy5Mno1KkTHn/8cUnmu9rzUnx8PGbNmoUOHTqgQ4cOmDVrFry8vBATEyNbhsrXi8pr+isLbFBQUKN+NkdtOcxmM0aPHo1du3bhhx9+gMPhEJ9D/f394e7u3mg5rpmCVzLUS2xsrACg2q+NGzdKOu9//vMfoW3btoK7u7twww03yH5J3caNG2v8/x0bGyvL/DXNDUBYvHixLPNXGj9+vPjfoWXLlsLtt98urF+/XtYMNZH70sIHHnhACA4OFgwGg2A2m4X77rtP2Ldvn2zzV/r++++Frl27CkajUYiMjBQWLVokewZBEIR169YJAISDBw8qMr/VahUmTZoktGnTRvDw8BAiIiKEl19+WbDZbLLm+Oqrr4SIiAjB3d1dCAoKEiZOnCicPXtWsvmu9rxUUVEhvP7660JQUJBgNBqFW2+9Vdi7d6+sGRYvXlzj919//XXZclRe1qjEa1d98RbGREREGsfPGSAiItI4lgEiIiKNYxkgIiLSOJYBIiIijWMZICIi0jiWASIiIo1jGSAiItI4lgEiIiKNYxkgIiLSOJYBIiIijWMZICIi0rj/D1o1IrtQ9HeEAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 600x514.286 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from vector_drawing import *\n",
    "angle = 37*pi/180\n",
    "print(angle)\n",
    "print(sin(37))\n",
    "print(cos(37))\n",
    "x,y = to_cartesian((15,angle))\n",
    "draw(\n",
    "    # 画点\n",
    "    Points(*[(x,y)]),\n",
    "    # 画箭头\n",
    "    Arrow((x,y))\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "x = (11.979532650709393 , 0)  y = (0 , 9.027225347280725)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.30：假设从原点出发，沿着从x轴正半轴逆时针旋转125°的方向移动8.5个单位，那么最终坐标是什么？已知sin(125°)=0.819、cos(125°)=-0.574，请画图来表示走过的角度和路径。***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "x = 8.5 * (-0.574) , y = 8.5 * 0.819"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-4.879, -6.961499999999999)\n"
     ]
    },
    {
     "data": {
      "image/png": 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Td999lw0bNvD+++9/4WmFirZme+xBy1NOBmDBt04PnEaSosV7EyhpFN1Yd8zAhv/9j7WTJgVOI0nRYRlQUun9yhQAlvzgQmo/+SRwGkmKBsuAkkpWmza0/9k1AMzab//AaSQpGiwDSjqtzzqLWE4OACvv+WPgNJKU/iwDSkp9pr0FwIrf/Ibq0tLAaSQpvVkGlJQycnLo8kDd3S7nDjmcBN5CQ5IizzKgpNX8oIPIG3gQAEsvGRU2jCSlMcuAklqXP/0JgLUvvEDFjBmB00hSerIMKKnFYjF6vvAvABaeOZz4xo2BE0lS+rEMKOnldOlC4fe/D8CCYUcFTiNJ6ccyoJTQ7tJRANSsWEHB9Olhw0hSmrEMKGVsOt2ww2OPU1NWFjiNJKUPy4BSRmaLFrT/1S8BmH/ooMBpJCl9WAaUUvKPPpqqwkIAPho3LnAaSUoPlgGlnAWX/RiA1Q/+mcoPPwycRpJSn2VAqScjg86PPALAvG98k3htbeBAkpTaLANKSc2+uictTzgegAVnnhk4jSSlNsuAUlbRzTcDsOG/77Bu8uTAaSQpdVkGlNJ6T/kPAIu/P5LaDRsCp5Gk1GQZUErLatuW9lddBcCsffcLnEaSUpNlQCmv9TlnQ2YmAKvu+1PgNJKUeiwDSgt93667RPHyX/2K6o8+CpxGklKLZUBpISM3l+L77gVg7mGDicfjgRNJUuqwDChttDjkEPIOOACAkh//OHAaSUodlgGllS5/fhCA8gnP8cl//xs4jSSlBsuA0kosFqPn888BsOD0M4hv3Bg4kSQlP8uA0k5Ot24Unj8CgLlDhwVOI0nJzzKgtNTusssA2FhaStkzzwROI0nJzTKgtNXnzTcAKPnp5dSUlwdOI0nJyzKgtJVZUEDRr38NwOwDBwROI0nJyzKgtNbym98gu6gIgI9++avAaSQpOVkGlPZ6vvAvAFb/6U9UzpsfOI0kJR/LgNJeLCuLbo8/BsC8Y4/16oSS9DmWAUXCbnvvTcE3vwnAwm+fHTiNJCUXy4Aio+hXvwTgk+nTWTfllcBpJCl5WAYUGbFYjF6TJwOw+IILqN2wIXAiSUoOlgFFSnb7drS74nIAZu23f+A0kpQcLAOKnMLzzqv7QzzOqgceCBlFkpKCZUCR1HfmDACW/+Jmqj9aHjiNJIVlGVAkZTRrRvEf/wjA3MMO83RDSZFmGVBktRh0KLvtX3fcQMlPLw+cRpLCsQwo0ro+/BAA5c8+yyfvvhs4jSSFYRlQpMViMXpMmADAgtO+RXzjxsCJJKnpWQYUebk9utP6O98B4MOjjwmcRpKanmVAAtpf/lMAqpcsoewf/wycRpKalmVA+lSfN6YCUHLZZdSsXRs4jSQ1HcuA9KnMli0p+uXNAMw+4MDAaSSp6VgGpM9oefzxZLVvD8DyW24JnEaSmoZlQPqcXi+9CMCqP95L1YIFYcNIUhOwDEifE8vKotujjwB1Zxd4dUJJ6c4yIG3Hbl/7GvlHHw3AonPPCxtGkhLMMiB9gU63/gaAijffZP1rrwVOI0mJYxmQvkAsFqPX5JcBWPTdEdRWVoYNJEkJYhmQdiC7fXva/eQyAGb17x84jSQlhmVA+hKFI0bU/aF6I6v//JewYSQpARJaBsaMGUMsFtvqo0OHDoncpJQQfWe8DcBHN93ExhUrAqeRpMaV8D0DX/3qVyktLd388a63iVUKythtN4r/cDcAcwZ9PXAaSWpcWQnfQFZWvfcGVFZWUvmZg7TKy8sBqK6uprq6OiH5UsWm5+8cws0h9+CDyd1nbyrfeZclP72c9jfe0OQZPsvXRB3nUMc5bLHp2iDxeDzS82jIc094GZgzZw5FRUXk5uYyYMAAbrrpJnr06LHddceNG8fYsWO3WT5p0iTy8vISHTUlTJw4MXSEpBBsDmeeSZ933mXtM8/wv65dqOzcOUyOz/A1Ucc51HEObP6lsrKykgkTJgROE05FRUW9143FE3h5teeee46Kigr69OnDRx99xA033MAHH3zAe++9R2Fh4Tbrb2/PQHFxMaWlpdtdP0qqq6uZOHEiQ4cOJTs7O3ScYJJhDlXz5rHohBMB6DlzBrHMzCA5kmEWycA51HEOW3Tr1o2SkhKKiopYEOFLipeXl9OmTRvKysooKCjY4boJ3TNwzDHHbP7z3nvvzcCBA+nZsycPPvggo0eP3mb93NxccnNzt1menZ0d+Rf3Js6iTsg5ZPftS+tzz2H1g39m8Qkn0vNfzwfJsTmPrwnAOWziHOquEbLpc5Rn0ZDn3qSnFjZv3py9996bOXPmNOVmpUbX/sorAahauJDy554LnEaSdk2TloHKykref/99Onbs2JSblRKiz9TXAVh66Whq1q0LnEaSdl5Cy8Bll13G5MmTmT9/Pm+88Qannnoq5eXlnHvuuYncrNQkMnffnY433QTA7P4HBE4jSTsvoWVgyZIlnHnmmfTt25eTTz6ZnJwcpk6dSteuXRO5WanJ7H7ySWS2aQPA8ttuCxtGknZSQg8gfOSRRxL546Wk0HvSv/lg731Ydfcf2P3kk8np0iV0JElqEO9NIO2iWHY2Xf86HoAPhx1FAs/WlaSEsAxIjSBvv/3IH3okAIs33dhIklKEZUBqJJ1uvx2A9a+9zvqpbwROI0n1ZxmQGkksFqPXpH8DsOi886itqgqcSJLqxzIgNaLsjh1p++nVNWcfOCBwGkmqH8uA1MjafO8CAOIbNrB6/PjAaSTpy1kGpATo+/Z0AD66/udsXLkycBpJ2jHLgJQAGXl5dL7zTgDmHDoocBpJ2jHLgJQg+YcPodlXvwpAyTXXBE4jSV/MMiAlULfHHwOg7G9PsOH99wOnkaTtswxICRTLyKDHs88AMP+kk4nX1AROJEnbsgxICZbbuzetzjoLgHnHnxA4jSRtyzIgNYEOP6s7ZqDqww8p/9cLgdNI0tYsA1IT6f36awAsveQSatatD5xGkrawDEhNJKtVKzre8HMAZvfvHziNJG1hGZCa0O6nnkrm7rsDsOKO34UNI0mfsgxITaz3lP8AsPL3v6dqyZLAaSTJMiA1uVh2Nl0ffgiAD48cSjweD5xIUtRZBqQA8vr1o8XhhwOw+HvfD5xGUtRZBqRAOv++7piB9VOmsP7NNwOnkRRllgEpkFgsRq+XXgRg0TnnEq+qCpxIUlRZBqSAsjt1ou2oSwCYPfDgwGkkRZVlQAqszciRANSuX8+aRx4NnEZSFFkGpCTQ9+3pACwbM4aNq1cHTiMpaiwDUhLIyMvbfEDhnIMPCZxGUtRYBqQkkX/EEeT27QtA6bXXBU4jKUosA1IS6f7UkwB8/NhjbJg1K3AaSVFhGZCSSCwjg+5PPw3A/BNOJF5bGziRpCiwDEhJplnfPux+xukAzD/xpMBpJEWBZUBKQh3HjAGgcvZs1r74YtgwktKeZUBKUr1fexWAJRf/kNr16wOnkZTOLANSkspq3ZoOY8cCMKtf/8BpJKUzy4CUxFqd/i0y8vMBWHHnnYHTSEpXlgEpyfV59RUAVt5+B1VLlgZOIykdWQakJBfLyaHrX/4MwIdHHkk8Hg+cSFK6sQxIKSDvgANoftjXAVjygwsDp5GUbiwDUooovvtuANa9/DIV06YFTiMpnVgGpBQRi8Xo+eJEABZ++2zi1dWBE0lKF5YBKYXkdO5Mm4svBmD+kMMDp5GULiwDUoppe/FFANSWlVHw5puB00hKB5YBKQX1nV53zECHJ56kZs2awGkkpTrLgJSCMpo3p8OtvwFg/tcPC5xGUqqzDEgpqsWRR1LZrh0Ay66/PnAaSanMMiClsIWXjgJgzfi/smH27LBhJKUsy4CUyjIyKP7b4wDMP/4E4rW1gQNJSkWWASnF5fbty+6nnQbA/FNPDZxGUiqyDEhpoOPP644ZqPy/91n7738HTiMp1VgGpDTR+9O7Gy658CJqKyoCp5GUSiwDUprIKiykw3XXAjBr/36B00hKJZYBKY20OvNMYrvtBsDKu/8QOI2kVGEZkNJMnzemArDittuoLikJnEZSKrAMSGkmIyeHLg8+CMDcw48gHo8HTiQp2VkGpDTUfMCBND/kEACW/PCHgdNISnaWASlNFd/7RwDWvfgSFW/PCJxGUjKzDEhpKhaL0XPiCwAsHD6ceHV14ESSklWTlYFx48YRi8UYNWpUU21Siryc4mLaXPgDAOYMHhI4jaRk1SRl4K233uKee+5hn332aYrNSfqMtj/6EQA1q1bx8RNPBk4jKRllJXoD69at46yzzuKPf/wjN9xwww7XrayspLKycvPj8vJyAKqrq6mO+C7OTc/fOTiHTRoyix6vv8a8gQdTevXVNPv6IDJ33z3B6ZqOr4k6zmGLTWfQxOPxSM+jIc89Fk/weUfnnnsurVu35tZbb2Xw4MHsu+++3Hbbbdtdd8yYMYwdO3ab5ePHjycvLy+RMaW01+Kddyh6eDwAs2/+ReA0UuKMGDGCVatWUVhYyH333Rc6TjAVFRUMHz6csrIyCgoKdrhuQvcMPPLII7z99tu89dZb9Vr/yiuvZPTo0Zsfl5eXU1xczJAhQygsLExUzJRQXV3NxIkTGTp0KNnZ2aHjBOMctmjwLI49loWvvkr1goUc8M47tL3iisSHbAK+Juo4hy1yc3M3fz722GMDpwln0971+khYGVi8eDGXXHIJL7zwAs2aNavX9+Tm5m7+S/ys7OzsyL+4N3EWdZzDFg2ZRc9//pMPvroXZQ+Pp/DMM8nt1SvB6ZqOr4k6zqHuTJpNn6M8i4Y894QdQDh9+nSWL19Ov379yMrKIisri8mTJ3P77beTlZVFTU1NojYt6QvEMjPp/uQTAMz75nHEa2sDJ5KUDBJWBo444gjeffddZs6cufmjf//+nHXWWcycOZPMzMxEbVrSDjTbc09annQSAAvOODNwGknJIGFvE+Tn57PXXntttax58+YUFhZus1xS0yoadxNlTz3FhnfeYe3LL5M/eHDoSJIC8gqEUkT1fmUKAEtG/oDaTz4JnEZSSE1aBl5++eUvPK1QUtPKatOG9tdcA8Cs/fYPnEZSSO4ZkCKs9bfPIvbpEcer7r03cBpJoVgGpIjrM30aAMt/fQvVy5YFTiMpBMuAFHEZOTl0uf9PAMwdPIQEX5RUUhKyDEii+cCB5B10EABLR10aOI2kpmYZkASwee/A2n/9i09mzgwbRlKTsgxIAuou3drzX88DdRcjim/cGDiRpKZiGZC0WU7XrhR+73sAzD38iMBpJDUVy4CkrbQbXXfMwMbly/n4738PG0ZSk7AMSNpGn7feBKD0iiupKSsLnEZSolkGJG0jMz+folt+DcDsAQcFTiMp0SwDkrar5Te+QXZxMQAf/eLmwGkkJZJlQNIX6vn8cwCsfuABKufNC5xGUqJYBiR9oVhmJt3+9jcA5h37DeK1tYETSUoEy4CkHdptr69ScPxxACwcflbgNJISwTIg6UsV3Vx3zMAnM2eybsqUwGkkNTbLgKQvFYvF6PWfyQAsvuB71G7YEDiRpMZkGZBUL9nt2tH+qisBmLXvfoHTSGpMlgFJ9db6nHMgo+5/G6v+dH/gNJIai2VAUoP0nfE2AMt/+UuqP/oocBpJjcEyIKlBMnJzKb73XgDmHjaYeDweOJGkXWUZkNRgLQ49hLz+/QEo+fFlgdNI2lWWAUk7pctf/gxA+YQJfPLOO4HTSNoVlgFJOyUWi9HjuQkALPjW6cQ3bgycSNLOsgxI2mm53btTeP4IAOYOGxY4jaSdZRmQtEvaXVZ3zMDGklLKnn02cBpJO8MyIGmX9XnzDQBKfvJTasrLA6eR1FCWAUm7LLOggKJf/RKA2QcOCJxGUkNZBiQ1ipbHHUdWUUcAPvrVrwKnkdQQlgFJjabXCy8AsPq+P1E5f37gNJLqyzIgqdHEsrLo9vhjAMw75livTiilCMuApEa12957U3DssQAsOvucwGkk1YdlQFKjK7rl1wBUTJvGuldeDZxG0pexDEhqdLFYjF6TXwZg8fnnU1tZGTaQpB2yDEhKiOz27Wl3+eUAzNq/X+A0knbEMiApYQq/c17dH2pqWP3nPwfNIumLWQYkJVTfmTMA+OimcVQvXx44jaTtsQxISqiMZs0o/uM9AMz9+mGebiglIcuApIRrMWgQu+27LwAlnx5HICl5WAYkNYmufx0PQPkzz/LJu/8LnEbSZ1kGJDWJWCxGjwkTAFhw2mnEa2oCJ5K0iWVAUpPJ7dGd1uedB8CHRx8TNoykzSwDkppU+yvqjhmoXryYsn/+M3AaSWAZkBRAnzemAlDy48uoWbs2cBpJlgFJTS6zZUs6/mIcALMPODBwGkmWAUlB7H7iiWS1awfA8t/cGjiNFG2WAUnB9Pr3SwCsuuceqhYuDJxGii7LgKRgYllZdHvkrwB8eNTRXp1QCsQyICmo3fbdl/yjjgJg0Xe+GziNFE2WAUnBdbqt7piBiqlTWf/664HTSNFjGZAUXCwWo9fLk4C6vQO1VVWBE0nRYhmQlBSyO3Sg3U8uA2B2/wMCp5GixTIgKWkUjhgBQLyqitUPPRw4jRQdlgFJSaXvjLcB+OiGG9i4YkXgNFI0WAYkJZWM3Xaj8913ATBn0NcDp5GiwTIgKenkDx5Ms733BqDkyqsCp5HSX0LLwF133cU+++xDQUEBBQUFDBw4kOeeey6Rm5SUJro9+ggAZU89xSfvvRc4jZTeEloGOnfuzC9+8QumTZvGtGnTOPzwwznhhBN4z/+wJX2JWEYGPf7xLAALTjmVeE1N4ERS+spK5A8/7rjjtnp84403ctdddzF16lS++tWvbrN+ZWUllZWVmx+Xl5cDUF1dTXV1dSKjJr1Nz985OIdNojCLjK5dafntsyh76GE+/MY36frsM9usE4U51Idz2GLTZa3j8Xik59GQ557QMvBZNTU1PP7446xfv56BAwdud51x48YxduzYbZZPmjSJvLy8REdMCRMnTgwdISk4hy3SfhZ7700foHrBAv7zi1+wbp99trta2s+hnpwDm3+prKysZMKECYHThFNRUVHvdWPxBN8Z5N1332XgwIFs2LCBFi1aMH78eI499tjtrru9PQPFxcWUlpZSWFiYyJhJr7q6mokTJzJ06FCys7NDxwnGOWwRpVnUlJUx/9BBAPR4/TUyWrTY/LUozWFHnMMW3bp1o6SkhKKiIhYsWBA6TjDl5eW0adOGsrIyCgoKdrhuwvcM9O3bl5kzZ/Lxxx/zxBNPcO655zJ58mT23HPPbdbNzc0lNzd3m+XZ2dmRf3Fv4izqOIctojCL7DZt6HjjjZRefTXzBh7MHh+8v+06EZhDfTiHustbb/oc5Vk05Lkn/NTCnJwcevXqRf/+/Rk3bhxf+9rX+O1vf5vozUpKM7ufcjKZn+4hXHH77YHTSOmlya8zEI/Ht3orQJLqq/enNzNaeeddVC1eHDiNlD4SWgauuuoqpkyZwoIFC3j33Xe5+uqrefnllznrrLMSuVlJaSqWnU3X8eMB+HDoMBJ8yJMUGQktAx999BFnn302ffv25YgjjuCNN97g+eefZ+jQoYncrKQ0lrf/fuQPPRKAxedfEDiNlB4SegDhfffdl8gfLymiOt1+Ox/ssSfrX32VijffDB1HSnnem0BSyonFYvT690sAlIw4n9jGjYETSanNMiApJWUXFdH20ksB6Dn2+sBppNRmGZCUstp8/3sAZFRVUfboo4HTSKnLMiAppfV4YyoAK264kY2rVgVOI6Umy4CklJaRl8fSc88BYM4hhwZOI6Umy4CklLd+zz3J3eMrAJT+7GeB00ipxzIgKS10fuQRAD5+/G9s+OCDwGmk1GIZkJQWYhkZdH/maQDmn3gS8drawImk1GEZkJQ2mvXpQ6vhwwGYf8IJgdNIqcMyICmtdLi27piByjlzKX/hhcBppNRgGZCUdnq//hoAS390CTXr1gdOIyU/y4CktJPVqhUdb/g5ALP79w+cRkp+lgFJaWn3U08lo2UBACt+9/vAaaTkZhmQlLb6TJkCwMrf/Y6qJUsCp5GSl2VAUtqK5eTQ9eGHAPjwyKHE4/HAiaTkZBmQlNby+vWjxZAhACweOTJwGik5WQYkpb3Od9YdM7B+8n+oeOutwGmk5GMZkJT2YrEYvV56EYCFZ59DvKoqcCIpuVgGJEVCdqdOtPnRDwGY7d0Npa1YBiRFRtsLLwSgdu1a1jz6WOA0UvKwDEiKlL7TpwGw7Lrr2Lh6deA0UnKwDEiKlIzmzen8uzsAmHPwIYHTSMnBMiApcvKPPJLcPn0AKB0zJmwYKQlYBiRFUve/PwXAx488yoZZswOnkcKyDEiKpFhGBt2f/jsA8084gXhtbdhAUkCWAUmR1axvX3Y//XQA5p98SuA0UjiWAUmR1nHsGAAqP/iAtS+9FDaMFIhlQFLk9X7tVQCWXHQxtevXB04jNT3LgKTIy2rdmg5jxwIwq1//wGmkpmcZkCSg1enfIqN5cwBW3n134DRS07IMSNKn+rz+GgArbvst1UuXBk4jNR3LgCR9KpaTQ5c/PwjA3COOJB6PB04kNQ3LgCR9RvMDD6T51wcBdQcUSlFgGZCkzyn+wx8AWPfvf1MxfXrgNFLiWQYk6XNisRg9X5wIwMKzvk28ujpwIimxLAOStB05nTvT5qKLAJgz6OuB00iJZRmQpC/Q9od1xwzUfPwxH//tb4HTSIljGZCkHegzbRoApdf8jI1r1gROIyWGZUCSdiCzRXM63f5bAOYMPDhwGikxLAOS9CUKhg0jp2dPAJb9/IbAaaTGZxmQpHro8czTAKx5+GEq58wJnEZqXJYBSaqHWGYm3Z96EoB5xx1PvLY2cCKp8VgGJKmemu2xBy1PPQWABad9K3AaqfFYBiSpAYpuqDtmYMN777F20qTAaaTGYRmQpAbq/eorACz5wYXUVlQETiPtOsuAJDVQVmEh7a/9GQCz9u8XOI206ywDkrQTWg8fTqxZMwBW3vPHwGmkXWMZkKSd1OfNNwBY8ZvfUF1aGjiNtPMsA5K0kzJycujywAMAzB1yOPF4PGwgaSdZBiRpFzQ/aADND667TPHSH10SOI20cywDkrSLiu+7F4C1EydSMWNG4DRSw1kGJGkXxWIxer7wLwAWnjmceHV14ERSw1gGJKkR5HTpQuEPRgIwZ8jhgdNIDWMZkKRG0u6SumMGalau5OMnnwqcRqo/y4AkNaI+094CoPSqq6j5+OOwYaR6SmgZGDduHAcccAD5+fm0a9eOE088kVmzZiVyk5IUVGaLFnS69TcAzD5oYOA0Uv0ktAxMnjyZiy66iKlTpzJx4kQ2btzIsGHDWL9+fSI3K0lBFRxzDDlduwKw7KabAqeRvlxWIn/4888/v9Xj+++/n3bt2jF9+nS+/vWvb7N+ZWUllZWVmx+Xl5cDUF1dTXXEj87d9Pydg3PYxFnUSdY5FD/9dz7cdz/W/Pkv5J9yCjk9eiR0e8k6hxA2XfwpHo9Heh4Nee6xeBNeMmvu3Ln07t2bd999l7322mubr48ZM4axY8dus3z8+PHk5eU1RURJajS5S5fS9fY7AJg97ibI8DCtpjBixAhWrVpFYWEh9913X+g4wVRUVDB8+HDKysooKCjY4bpNVgbi8TgnnHACa9asYcqUKdtdZ3t7BoqLiyktLaWwsLApYiat6upqJk6cyNChQ8nOzg4dJxjnsIWzqJPsc/jo6mtY+8wz5O6zN8UPP5yw7ST7HJpSt27dKCkpoaioiAULFoSOE0x5eTlt2rSpVxlI6NsEn3XxxRfzzjvv8Morr3zhOrm5ueTm5m6zPDs7O/Iv7k2cRR3nsIWzqJOsc+j8y5t5/5lnqHznXSpfe40Whx2W0O0l6xyaUiwW2/w5yrNoyHNvkn1WP/zhD3nmmWeYNGkSnTt3bopNSlLS6D3lPwAs/v5Iaj/5JHAaaVsJLQPxeJyLL76YJ598kn//+9907949kZuTpKSU1bYt7a++GoBZ++0fOI20rYSWgYsuuoiHHnqI8ePHk5+fz7Jly1i2bBmf2IwlRUzrs78N2XXvzK6K8EFtSk4JLQN33XUXZWVlDB48mI4dO27+ePTRRxO5WUlKSn2nTQNg+a9+TfWyZYHTSFsk/G2C7X2cd955idysJCWljNxcuvypbq/A3MFDaMIzu6Ud8qRXSWpCzQ8+mLwDDwRg6ejRgdNIdSwDktTEujz4AABrn3ueT/7737BhJCwDktTkYrEYPZ9/DoAFp59BfOPGwIkUdZYBSQogp1s3Ci+4AIC5RxwZOI2izjIgSYG0+3HdMQMbP/qIsqefDpxGUWYZkKSA+rz1JgAll19BTVlZ4DSKKsuAJAWUmZ9P0a9/DcDsAQcFTqOosgxIUmAtv/kNsj+9b8tHN/8ycBpFkWVAkpJAz389D8Dq+++nct78wGkUNZYBSUoCscxMuj3+OADzjj3WqxOqSVkGJClJ7Lb3XhQcdxwAC8/6duA0ihLLgCQlkaJf3gzAJ2+/zboprwROo6iwDEhSEonFYvT6z2QAFl9wAbUbNgROpCiwDEhSkslu1472V14BwKx99wucRlFgGZCkJNT63HMhFgNg1QMPhA2jtGcZkKQk1XfmDACW/+Jmqj9aHjiN0pllQJKSVEZuLsX33gvA3MMO83RDJYxlQJKSWItDD2G3fv0AKPnJTwOnUbqyDEhSkuv60F8AKP/HP/jk3XcDp1E6sgxIUpKLxWL0eG4CAAtO+xbxjRsDJ1K6sQxIUgrI7d6d1iO+C8CHRx0dOI3SjWVAklJE+5/8BIDqpUspe/YfgdMonVgGJCmF9HnzDQBKfvITasrLA6dRurAMSFIKySwo2Hz/gtkHDgicRunCMiBJKabl8ceT1aEDAMtvuSVwGqUDy4AkpaBeL04EYNUf76VqwYKwYZTyLAOSlIJiWVl0e+xRAD48+hivTqhdYhmQpBS12z77UHDsMQAs/e6IwGmUyiwDkpTCij49ZmDDtGnkzZ4TOI1SlWVAklJYLBaj1+SXAeh8333UVlaGDaSUZBmQpBSX3b49hZf9GIB5Bw0MnEapyDIgSWmg1bnn1v1h40ZW//kvYcMo5VgGJClNzLnh5wB8dNNNbFyxInAapRLLgCSliXh2Nh3v/D0AcwZ9PXAapRLLgCSlkeaDBrHb174GQMnlVwROo1RhGZCkNNP1r+MBKHv6aT7533uB0ygVWAYkKc3EMjLo8c+6WxwvOPVU4jU1gRMp2VkGJCkN5fbsSetPzzD48NhjA6dRsrMMSFKaan9l3TED1QsXUT5hQuA0SmaWAUlKY33emArA0tE/pmbdusBplKwsA5KUxjJbtqTjuHEAzO5/QOA0SlaWAUlKc7ufdCKZbdsAsPzW28KGUVKyDEhSBPSeNAmAVX/4A1WLFgVOo2RjGZCkCIhlZdHtkb8C8OGwo4jH44ETKZlYBiQpInbbd1/yjzoKgMUjRgROo2RiGZCkCOl0260ArH/tddZPnRo4jZKFZUCSIiQWi9Hr5brjBxad9x1qq6oCJ1IysAxIUsRkd+hA2x+PBmD2AQcGTqNkYBmQpAhqc8EFAMQrK1n98MOB0yg0y4AkRVTfGW8D8NHPb2DjypWB0ygky4AkRVTGbrvR+e67AJhz6KDAaRSSZUCSIix/8GCa7bUXACVXXx04jUKxDEhSxHV77FEAyp54kg3/93+B0ygEy4AkRVwsI4Me/3gWgPknn0K8piZwIjU1y4AkidxevWj17W8DMO+44wOnUVNLaBn4z3/+w3HHHUdRURGxWIy///3vidycJGkXdLim7piBqnnzKH/+X4HTqCkltAysX7+er33ta/zud79L5GYkSY2k9+uvAbB01Chq1q0PnEZNJSuRP/yYY47hmGOOqff6lZWVVFZWbn5cXl4OQHV1NdXV1Y2eL5Vsev7OwTls4izqOIc6jTaHFi1od/31LL/2Wmb370+vd99phHRNa9MdGePxeKRfFw157gktAw01btw4xo4du83ySZMmkZeXFyBR8pk4cWLoCEnBOWzhLOo4hzqNMofcHHo0b07W+vW8MepSVg0buus/swlt+qWysrKSCRMmBE4TTkVFRb3XjcWb6KbWsViMp556ihNPPPEL19nenoHi4mJKS0spLCxsgpTJq7q6mokTJzJ06FCys7NDxwnGOWzhLOo4hzqNPYd4dTUf7t8PgK4TJpBd3HmXf2ZT6datGyUlJRQVFbFgwYLQcYIpLy+nTZs2lJWVUVBQsMN1k2rPQG5uLrm5udssz87OjvR/5J/lLOo4hy2cRR3nUKfR5pCdTdfxD7Nw+FksPPZYvvL+/xGLxXb95zaBTTljsVikXxMNee6eWihJ2q68/fenxRFHALD4e98PnEaJZBmQJH2hzr+7A4D1U6aw/s03A6dRoiS0DKxbt46ZM2cyc+ZMAObPn8/MmTNZtGhRIjcrSWoksViMXv9+CYBF55xLvKoqcCIlQkLLwLRp09hvv/3Yb7/9ABg9ejT77bcf1157bSI3K0lqRNlFRbQdNQqA2QcNDBtGCZHQMjB48GDi8fg2Hw888EAiNytJamRtRtYdM1BbUcGaRx4JnEaNzWMGJEn10vft6QAsGzOWjatWBU6jxmQZkCTVS0ZeHp3v/D0Acw45NHAaNSbLgCSp3vIPP5zcPfYAoPTa6wKnUWOxDEiSGqT7E38D4OPHHmPDrFmB06gxWAYkSQ0Sy8ig+zNPAzD/hBOJ19YGTqRdZRmQJDVYsz59aDX8TKCuECi1WQYkSTulw6fXjKmcM4dy7xqZ0iwDkqSd1vv11wBY+sMfUbt+feA02lmWAUnSTstq1YoOP78egFn9+gdOo51lGZAk7ZJWp51GRkEBACt+//vAabQzLAOSpF3W55UpAKy843dULVkaOI0ayjIgSdplsZwcuj70FwA+PPJI4vF44ERqCMuAJKlR5PXvT4vDDgNgycgfBE6jhrAMSJIaTee77wJg3eTJVEybFjiN6ssyIElqNLFYjJ4vvgjAwm+fTbyqKnAi1YdlQJLUqHI6d6LNDy8GYPagQYHTqD4sA5KkRtf2oosAqC0rZ83jjwdOoy9jGZAkJUTf6XXHDCz72bVsXLMmcBrtiGVAkpQQGc2b0+mO2wGYM/DgwGm0I5YBSVLCFAwdSm7v3gCUjh0bOI2+iGVAkpRQ3Z/+OwAf//URNsyeHTaMtssyIElKqFhGxuZCMP/4E4jX1oYNpG1YBiRJCdesb192/9a3AJh/yqmB0+jzLAOSpCbR8fq6YwYq33+ftS+9FDiNPssyIElqMr1ffQWAJRddTG1FReA02sQyIElqMlmFhXQYMwaAWfv3CxtGm1kGJElNqtUZp5ORlwfAyrv/EDiNwDIgSQqgz9TXAVhx221Ul5QETiPLgCSpycVycujy4IMAzD38COLxeOBE0WYZkCQF0XzAgTQ/9FAAllz8w8Bpos0yIEkKpviP9wCw7qWXqHj77cBpossyIEkKJhaL0fPFiQAsHH4W8erqwImiyTIgSQoqp3Nn2lx4IQBzDhscNkxEWQYkScG1/VHdMQM1q1fz8RNPBk4TPZYBSVJS6DNtGgClV1/NxjVrAqeJFsuAJCkpZLZoTqfbbgNgzsCDw4aJGMuAJClpFBx9FDk9egCw7IYbA6eJDsuAJCmp9Hj2GQDWPPQQlXPnBk4TDZYBSVJSiWVm0v2puoMI533zOOK1tYETpT/LgCQp6TTbYw9annIyAAtOPyNwmvRnGZAkJaWiG+uOGdjw7rusnTQpcJr0ZhmQJCWt3q9MAWDJDy6k9pNPAqdJX5YBSVLSymrThvbX/gyAWfvtHzhN+rIMSJKSWuvhw4nl5gKw6t57A6dJT5YBSVLS6/PWmwAs//UtVC9bFjhN+rEMSJKSXkZODl0euB+AuYOHEI/HAydKL5YBSVJKaH7QQeQNPAiApaMuDZwmvVgGJEkpo8uf/gTA2n/9i4oZMwKnSR+WAUlSyojFYvR84V8ALDxzOPGNGwMnSg+WAUlSSsnp0oXCkd8HYO6QwwOnSQ+WAUlSymk3ahQAG1es4OO//z1olnRgGZAkpaQ+094CoPSKK6kpKwucJrVZBiRJKSmzRQs6/eYWAGYPOChwmtRmGZAkpayCY48lu2sXAOZefc1211myZAll7jnYIcuAJCmltfnrXwGofuIJFr766lZfW7x4MYcddhhHH320hWAHmqQM3HnnnXTv3p1mzZrRr18/pkyZ0hSblSRFwLqKCi6prgagYsT5bPz0dMOamhoGDx7MvHnzWL58OWvXrg0ZM6klvAw8+uijjBo1iquvvpoZM2YwaNAgjjnmGBYtWpToTUuSIqBz587c9/IkXqqtAaB61SoAVqxYwbx58+jRowcvv/wynTt3DhkzqcXiCb7A84ABA9h///256667Ni/bY489OPHEExk3btxW61ZWVlJZWbn5cXl5OcXFxXTo0IHMzMxExkx68XicyspKcnNzicVioeME4xy2cBZ1nEMd51C3JyC+ciUrNm6k9tNlmZmZtG3bNpL/htTW1lJaWkpZWRkFBQU7XDcrkUGqqqqYPn06V1xxxVbLhw0bxmuvvbbN+uPGjWPs2LHbLF/mHaokSTuhpqbGf0PqIaFlYOXKldTU1NC+ffutlrdv3367fzlXXnklo0eP3vzYPQNb2PrrOIctnEUd51DHOdT9w79ixQpqamo2L3PPQGm91k1oGdjk8y/MeDy+3Rdrbm4uubm52yz/3//+R2FhYcLypYLq6momTJjAscceS3Z2dug4wTiHLZxFHedQJ+pzWLx4MYMHD6ampobMzMytPufl5fHyyy9TXFwcOmaTKi8vp2XLlvVaN6EHELZp04bMzMxt9gIsX758m70FkiTtjCVLlmw+a6BHjx60bdsWgLZt29KjRw/mzZvH4MGDWbJkSeCkySuhZSAnJ4d+/foxceLErZZPnDiRgw8+OJGbliRFRH5+Pu3atdt81sCmtwQyMzN5+eWX6dGjB+3atSM/Pz9w0uSV8LcJRo8ezdlnn03//v0ZOHAg99xzD4sWLWLkyJGJ3rQkKQJatmzJ888/z9q1a7c5fbC4uJjJkyeTn59f713mUZTwMnD66aezatUqrr/+ekpLS9lrr72YMGECXbt2TfSmJUkR0bJlyy/8x97rC3y5JjmA8MILL+TCCy9sik1JkqQG8t4EkiRFnGVAkqSIswxIkhRxlgFJkiLOMiBJUsRZBiRJijjLgCRJEWcZkCQp4iwDkiRFnGVAkqSIswxIkhRxlgFJkiLOMiBJUsRZBiRJijjLgCRJEWcZkCQp4iwDkiRFnGVAkqSIswxIkhRxlgFJkiLOMiBJUsRZBiRJijjLgCRJEWcZkCQp4iwDkiRFnGVAkqSIswxIkhRxlgFJkiLOMiBJUsRZBiRJijjLgCRJEWcZkCQp4iwDkiRFnGVAkqSIswxIkhRxlgFJkiLOMiBJUsRZBiRJijjLgCRJEWcZkCQp4iwDkiRFnGVAkqSIswxIkhRxlgFJkiLOMiBJUsRZBiRJijjLgCRJEWcZkCQp4iwDkiRFnGVAkqSIswxIkhRxlgFJkiLOMiBJUsRZBiRJijjLgCRJEZfQMnDjjTdy8MEHk5eXx+67757ITUmSpJ2U0DJQVVXFaaedxg9+8INEbkaSJO2CrET+8LFjxwLwwAMP1Gv9yspKKisrNz8uKysDYPXq1Y2eLdVUV1dTUVHBqlWryM7ODh0nGOewhbOo4xzqOIctampqNn9etWpV4DThrF27FoB4PP6l6ya0DDTUuHHjNheIz+rTp0+ANJKkVLZs2TLatGkTOkZwa9eupWXLljtcJ6nKwJVXXsno0aM3P/7444/p2rUrixYt+tInku7Ky8spLi5m8eLFFBQUhI4TjHPYwlnUcQ51nMMWzqJOPB5n7dq1FBUVfem6DS4DY8aM2e5v75/11ltv0b9//4b+aHJzc8nNzd1mecuWLSP9F/pZBQUFzgLn8FnOoo5zqOMctnAW1PsX6QaXgYsvvpgzzjhjh+t069atoT9WkiQF0uAy0KZNG9+DkSQpjST0mIFFixaxevVqFi1aRE1NDTNnzgSgV69etGjR4ku/Pzc3l+uuu267bx1EjbOo4xy2cBZ1nEMd57CFs2i4WLw+5xzspPPOO48HH3xwm+WTJk1i8ODBidqsJElqgISWAUmSlPy8N4EkSRFnGZAkKeIsA5IkRZxlQJKkiEupMvDPf/6TAQMGsNtuu9GmTRtOPvnk0JGC6NatG7FYbKuPK664InSsYCorK9l3332JxWKbT1+NmuOPP54uXbrQrFkzOnbsyNlnn01JSUnoWE1qwYIFjBgxgu7du7PbbrvRs2dPrrvuOqqqqkJHCyKqt5C/88476d69O82aNaNfv35MmTIldKSUkDJl4IknnuDss8/mO9/5Dv/973959dVXGT58eOhYwVx//fWUlpZu/rjmmmtCRwrmpz/9ab2uvZ3OhgwZwmOPPcasWbN44okn+PDDDzn11FNDx2pSH3zwAbW1tfzhD3/gvffe49Zbb+Xuu+/mqquuCh0tiCjeQv7RRx9l1KhRXH311cyYMYNBgwZxzDHHsGjRotDRkl88BVRXV8c7deoUv/fee0NHSQpdu3aN33rrraFjJIUJEybEv/KVr8Tfe++9OBCfMWNG6EhJ4emnn47HYrF4VVVV6ChB/fKXv4x37949dIyg7r///njLli1Dx2gSBx54YHzkyJFbLfvKV74Sv+KKKwIlSh0psWfg7bffZunSpWRkZLDffvvRsWNHjjnmGN57773Q0YK5+eabKSwsZN999+XGG2+M5K7Qjz76iAsuuIC//OUv5OXlhY6TNFavXs3DDz/MwQcfHPn72peVldG6devQMdQEqqqqmD59OsOGDdtq+bBhw3jttdcCpUodKVEG5s2bB9TdMfGaa67hH//4B61ateKwww5j9erVgdM1vUsuuYRHHnmESZMmcfHFF3Pbbbdx4YUXho7VpOLxOOeddx4jR47cqTtkpqPLL7+c5s2bU1hYyKJFi3j66adDRwrqww8/5I477mDkyJGho6gJrFy5kpqaGtq3b7/V8vbt27Ns2bJAqVJH0DIwZsyYbQ6E+/zHtGnTqK2tBeDqq6/mlFNOoV+/ftx///3EYjEef/zxkE+h0dR3FgCXXnophx12GPvssw/nn38+d999N/fddx+rVq0K/Cx2XX3ncMcdd1BeXs6VV14ZOnLCNOQ1AfCTn/yEGTNm8MILL5CZmck555xDPA0uMNrQOQCUlJRw9NFHc9ppp3H++ecHSt74dmYWUROLxbZ6HI/Ht1mmbQW9HPHKlStZuXLlDtfp1q0br7/+OocffjhTpkzh0EMP3fy1AQMGcOSRR3LjjTcmOmrC1XcWzZo122b50qVL6dy5M1OnTmXAgAGJitgk6juHM844g2effXar/8hramrIzMzkrLPO2u49MVLNrrwmlixZQnFxMa+99hoDBw5MVMQm0dA5lJSUMGTIEAYMGMADDzxARkZK7ACtl515TTzwwAOMGjWKjz/+OMHpwqqqqiIvL4/HH3+ck046afPySy65hJkzZzJ58uSA6ZJfQu9a+GXqezvkfv36kZuby6xZszaXgerqahYsWEDXrl0THbNJ7MqtoWfMmAFAx44dGzNSEPWdw+23384NN9yw+XFJSQlHHXUUjz76aMoXok125TWxqeNXVlY2ZqQgGjKHpUuXMmTIkM17D9OpCIC3kN+RnJwc+vXrx8SJE7cqAxMnTuSEE04ImCw1BC0D9VVQUMDIkSO57rrrKC4upmvXrvzqV78C4LTTTgucrmm9/vrrTJ06lSFDhtCyZUveeustLr300s3nmUfF55/rplti9+zZk86dO4eIFMybb77Jm2++yaGHHkqrVq2YN28e1157LT179kz5vQINUVJSwuDBg+nSpQu//vWvWbFixeavdejQIWCyMHb1FvKpaPTo0Zx99tn079+fgQMHcs8997Bo0SKPG6mPkKcyNERVVVX8xz/+cbxdu3bx/Pz8+JFHHhn/3//+FzpWk5s+fXp8wIAB8ZYtW8abNWsW79u3b/y6666Lr1+/PnS0oObPnx/ZUwvfeeed+JAhQ+KtW7eO5+bmxrt16xYfOXJkfMmSJaGjNan7778/Dmz3I4rOPffc7c5i0qRJoaMl1O9///t4165d4zk5OfH9998/Pnny5NCRUoK3MJYkKeLS6w01SZLUYJYBSZIizjIgSVLEWQYkSYo4y4AkSRFnGZAkKeIsA5IkRZxlQJKkiLMMSJIUcZYBSZIizjIgSVLE/T9sMc2NCk2ZBAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 600x771.429 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "print((8.5*(-0.574),-8.5 * 0.819))\n",
    "draw(\n",
    "    # 画点\n",
    "    Points(*[(8.5*(-0.574),8.5 * 0.819)]),\n",
    "    # 画箭头\n",
    "    Arrow((8.5*(-0.574),8.5 * 0.819))\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.31：0°、90°和180°的正弦和余弦各是多少？换句话说，在这些方向上，每单位距离经过多少个垂直和水平单位？***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "解：对于0°，没有垂直距离，所以sin(0°)=0；而每移动1个单位的距离就经过x轴正半轴方向上的1个单位，所以cos(0°)=1。\n",
    "对于90°（逆时针转1/4圈），每移动1个单位的距离就经过y轴正半轴方向上的1个单位，所以sin(90°)=1，而cos(90°)=0。\n",
    "最后，对于180°，每移动1个单位的距离都经过x轴负半轴方向上的1个单位，所以cos(180°)=-1，而cos(180°)=0。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.32：图2-48对于一个直角三角形给出了一些精确的测量数据。首先，确认这些长度在直角三角形中的有效性，因为它们必须满足勾股定理。然后，用图中的数据计算sin(30°)、cos(30°)和tan(30°)的值，精确到小数点后三位。***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![jupyter](../images/img2-8.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "解：\n",
    "$\\sqrt{(1/2)^2 + (\\sqrt{3}/2)^2}$ = $\\sqrt{4/1 + 3/4}$ = $\\sqrt{4/4}$ =1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "x = length * cos(30°)，y = length * sin(30°)，tan(30°) = sin(30°)/cos(30°)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "cos(30°) = x/length , sin(30°) = y/length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x= 0.866 y= 0.5\n",
      "cos= 0.866 sin= 0.5 tan= 0.577\n"
     ]
    }
   ],
   "source": [
    "x = round(sqrt(3)/2,3)\n",
    "y = round(1/2,3)\n",
    "\n",
    "cos1 = round(x/1,3)\n",
    "sin1 = round(y/1,3)\n",
    "tan1 = round(sin1/cos1,3)\n",
    "\n",
    "print(\"x=\",x,\"y=\",y)\n",
    "print(\"cos=\",cos1,\"sin=\",sin1,\"tan=\",tan1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.33：从另一个角度观察上一个练习中的三角形，用它计算sin(60°)、cos(60°)和tan(60°)的值，精确到小数点后三位。***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x= 0.5 y= 0.866\n",
      "cos= 0.5 sin= 0.866 tan= 1.732\n"
     ]
    }
   ],
   "source": [
    "y = round(sqrt(3)/2,3)\n",
    "x = round(1/2,3)\n",
    "\n",
    "cos1 = round(x/1,3)\n",
    "sin1 = round(y/1,3)\n",
    "tan1 = round(sin1/cos1,3)\n",
    "\n",
    "print(\"x=\",x,\"y=\",y)\n",
    "print(\"cos=\",cos1,\"sin=\",sin1,\"tan=\",tan1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.34：已知cos(50°)的余弦值是0.643。sin(50°)的值是多少，tan(50°)的值又是多少？通过画图来计算。***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.19175359259421\n",
      "1.1917535925942098\n"
     ]
    }
   ],
   "source": [
    "cospi = 50*pi/180\n",
    "sinpi = 50*pi/180\n",
    "\n",
    "\n",
    "print(tan(50*pi/180))\n",
    "print(sin(sinpi)/cos(cospi))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.35：116.57°对应的弧度是多少？用Python计算这个角的正切值，并确认它约等于-2。***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.03453030904979\n",
      "-1.9995682083189954\n"
     ]
    }
   ],
   "source": [
    "print(116.57*pi/180)\n",
    "# 正切值\n",
    "print(sin(116.57*pi/180) / cos(116.57*pi/180))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.36：cos(10π/6)和sin(10π/6)的值为正还是为负？使用Python计算它们的值并确认。***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8660254037844387 0.49999999999999994\n"
     ]
    }
   ],
   "source": [
    "print(cos(10*pi/60),sin(10*pi/60) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.37：用下面的列表推导式创建1000个极坐标对应的点。\n",
    "在Python代码中，将这些点转换为笛卡儿坐标，并用线段依次将其连接起来，从而画出一幅画。***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[(cos(5*x*pi/500.0), 2*pi*x/1000.0) for x in range(0,1000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to_cartesian\n",
    "polar_coords = [(cos(5*pi*x/500.0), 2*pi*x/1000.0) for x in range(0,1000)]\n",
    "dino_vectors = [to_cartesian(v) for v in polar_coords]\n",
    "\n",
    "draw(\n",
    "    Points(*dino_vectors, color = blue),\n",
    "    Polygon(*dino_vectors, color = blue),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.38：通过“猜测检查法”（guess-and-check）找出(-2, 3)对应的弧度（见图2-52）。提示：显然答案在π/2和π之间。在这个区间内，正切的绝对值总是随着弧度的增大而减小。***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![jupyter](../images/img2-6.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "解：已知条件x=-2,y=3,r=$\\sqrt{13}$。正切的绝对值总是随着弧度的增大而减小，这句话是因为sin随着弧度的增加而减小，tan=sin/cos。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\sqrt{13}*sin(\\Theta) =3 $ => $sin(\\Theta) = 3 / \\sqrt{13}$,$\\sqrt{13}*cos(\\Theta) =3-2 $ => $cos(\\Theta) = -2 / \\sqrt{13}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$tan(\\Theta) = (3 / \\sqrt{13}) / (-2 / \\sqrt{13}) = -3/2 = -1.5$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "所以需要找到tan($\\Theta$)=-1.5的$\\Theta$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.5289797578045667\n",
      "-1.5256470732011935\n",
      "-1.5223245421115472\n",
      "-1.5190121115901656\n",
      "-1.5157097290532848\n",
      "-1.5124173422757465\n",
      "-1.5091348993879299\n",
      "-1.5058623488727219\n",
      "-1.5025996395625056\n",
      "-1.4993467206361923\n",
      "-1.496103541616277\n",
      "-1.49287005236593\n"
     ]
    }
   ],
   "source": [
    "from math import atan,degrees\n",
    "to_polar((-2,3))\n",
    "print(tan(2.150))\n",
    "print(tan(2.151))\n",
    "print(tan(2.152))\n",
    "print(tan(2.153))\n",
    "print(tan(2.154))\n",
    "print(tan(2.155))\n",
    "print(tan(2.156))\n",
    "print(tan(2.157))\n",
    "print(tan(2.158))\n",
    "print(tan(2.159))\n",
    "print(tan(2.160))\n",
    "print(tan(2.161))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.39：在平面上找到另一个与$\\Theta$有相同正切值（即-3/2）的点。使用Python的反正切函数math.atan来求这个点的弧度值。***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.982793723247329 -56.309932474020215\n"
     ]
    }
   ],
   "source": [
    "# atan()返回的是弧度\n",
    "print(atan(-1.5),degrees(atan(-1.5)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.40：不使用Python，算出笛卡儿坐标(1, 1)和(1, -1)对应的极坐标。找到答案之后，使用to_polar来检查一下。***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "解：距离 = $\\sqrt{1^2 + 1^2} = \\sqrt{2}$,$tan(\\Theta) = (y / \\sqrt{2}) / (x / \\sqrt{2}) = y / x = 1 /1 = 1$,而因为tan(45°) = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "得：(1,1) 的极坐标是($\\sqrt{2}$ , 45°)，(1,-1) 的极坐标是($\\sqrt{2}$ , -45°)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7853981633974483\n",
      "0.9999999999999999\n",
      "0.9999999999999999\n",
      "0.7853981633974483\n",
      "45.0\n"
     ]
    }
   ],
   "source": [
    "from math import radians\n",
    "\n",
    "print(radians(45))\n",
    "print(tan(radians(45)))\n",
    "print(tan(45*pi/180))\n",
    "print(atan(1))\n",
    "print(0.7853981633974483* 180/pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1.4142135623730951, 0.7853981633974483)\n",
      "(1.4142135623730951, -0.7853981633974483)\n"
     ]
    }
   ],
   "source": [
    "print(to_polar((1,1)))\n",
    "print(to_polar((1,-1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.41（小项目）：如图2-53所示，恐龙嘴巴的夹角是多少？脚趾的夹角是多少？尾巴的夹角是多少？***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![jupyter](../images/img2-9.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "解：(1) 脚趾：以点(-1,4)为原点，(0,-3)为目标点。得(1,1)。r = $\\sqrt{1^2 + 1^2} = \\sqrt{2}$ ,tan($\\Theta$) = 1, $\\Theta$ = 45°"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(2) 嘴巴：以点(-2,2)为原点，(-5,1)为目标点。得(-3,-1),取相反坐标得(3,1)。r = $\\sqrt{3^2 + 1^2} = \\sqrt{10}$ ,tan($\\Theta$) = 1/3 ≈ 0.3, $\\Theta$ ≈ 17°"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(3) 尾巴：角一：以点(3,1)为原点，(6,4)为目标点。得(3,3),根据(1)得$\\Theta$ = 45°。角二：又以(5,1)为原点，(6,4)为目标点。得(1,3),得$\\Theta$ = 71°。角二是外角，所以需要：180°- 71° = 109°。而因为三角形的内角和等于180°，所以尾巴的角度得：180°- (109°+ 45°) = 26°"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2914567944778671\n",
      "16.69924423399362\n",
      "1.2490457723982544\n",
      "71.56505117707799\n"
     ]
    }
   ],
   "source": [
    "print(atan(0.3))\n",
    "print(atan(0.3)* 180/pi)\n",
    "\n",
    "print(atan(3))\n",
    "print(atan(3)* 180/pi)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 向量集合的变换"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 将小恐龙逆时针旋转pi/4\n",
    "rotation_angle = pi /4\n",
    "dino_vectors = [(6,4),(3,1),(1,2),(-1,5),(-2,5),(-3,4),(-4,4),(-5,3),(-5,2),(-2,2),(-5,1),(-4,0),(-2,1),(-1,0),(0,-3),(-1,-4),(1,-4),(2,-3),(1,-2),(3,-1),(5,1)]\n",
    "dino_polar = [to_polar(v) for v in dino_vectors]\n",
    "dino_rotated_polar = [(l,angle + rotation_angle) for l,angle in dino_polar]\n",
    "dino_rotated = [to_cartesian(p) for p in dino_rotated_polar]\n",
    "draw(\n",
    "    Polygon(*dino_vectors, color=gray),\n",
    "    Polygon(*dino_rotated, color=red),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 平移函数\n",
    "def translate(translation, vectors):\n",
    "    return [(v[0]+translation[0] , v[1]+translation[1]) for v in vectors]\n",
    "#return [add(translation,v) for v in vectors]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.42：实现rotate(angle, vectors)函数，接收笛卡儿坐标向量数组，并将这些向量旋转指定的角度（根据角度的正负来确定是逆时针还是顺时针）。***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 旋转函数\n",
    "def rotate(angle, vectors):\n",
    "    # 先把笛卡尔坐标转为极坐标\n",
    "    polar_42 = to_polar(vectors)\n",
    "    \n",
    "    # 将角度转为弧度\n",
    "    radian_42 = angle*pi / 180\n",
    "    \n",
    "    # 极坐标添加角度\n",
    "    polar_4 = (polar_42[0],polar_42[1]+radian_42)\n",
    "    \n",
    "    # 极坐标转笛卡尔坐标\n",
    "    return to_cartesian(polar_4)\n",
    "\n",
    "# 旋转函数\n",
    "def rotate1(angle, vectors):\n",
    "    # 先把笛卡尔坐标转为极坐标\n",
    "    polar_42 = to_polar(vectors)\n",
    "    \n",
    "    \n",
    "    # 极坐标添加角度\n",
    "    polar_4 = (polar_42[0],polar_42[1]+angle)\n",
    "    \n",
    "    # 极坐标转笛卡尔坐标\n",
    "    return to_cartesian(polar_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x763.636 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_dino = [rotate(90,p) for p in dino_vectors]\n",
    "draw(\n",
    "    Polygon(*new_dino, color=gray),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***练习2.43：实现函数regular_polygon(n)，返回一个规则n边形（即所有角和边长都相等）各顶点的笛卡儿坐标。例如，polygon(7)返回如图2-57所定义七边形的顶点向量。提示：在图2-57中，基于原点对向量(1, 0)进行6次均匀的旋转，从而得到了各个顶点。***\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![jupyter](../images/img2-10.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 传入n,返回n边形\n",
    "def regular_polygon(n):\n",
    "    return [to_cartesian((1 , 2*pi*k/n)) for k in range(0,n)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***(1) 写这个习题时，一开始的想法就是错的，因为我总想怎么把长度控制在(-1,0)到(1,0)之间，但其实只需要把极坐标的长度固定1就可以了。***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***(2) 算角度也是一样，这个问题本质是将一个圆的边分成几份(这个好像是以前算pi的方法)，也就是把2pi乘以当前部分索引(k)再除以总边数然后再不断旋转，来获取划分的点，再将点连接起来就是多边形了***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***(3) 对（2）的补充：以原点到(0,1)的线,逆时针旋转多大角度，以下为例子n=3***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. 当 n = 3 时，表示一个正三角形。我们可以使用表达式 2 * math.pi * k / n 来计算正三角形每个顶点的角度。\n",
    "2. 当 n = 3 时，k 的取值范围是 0 到 2。那么，表达式 2 * math.pi * k / n 的计算结果如下：\n",
    "3. 当 k = 0 时，角度为 0 * 2π/3 = 0 弧度，即起始位置。\n",
    "4. 当 k = 1 时，角度为 1 * 2π/3 = 2π/3 弧度，即约 120 度。\n",
    "5. 当 k = 2 时，角度为 2 * 2π/3 = 4π/3 弧度，即约 240 度。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.1887902047863905\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_dino = regular_polygon(3)\n",
    "print((2*pi*2/3))\n",
    "draw(\n",
    "    Polygon(*new_dino, color=gray),\n",
    "    Points(*new_dino)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ***练习2.44：先将恐龙按向量(8, 8)平移，再将其旋转5π/3（见图2-58），结果是什么？和先旋转再平移的结果一样吗？***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![jupyter](../images/img2-11.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x555.556 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 先旋转再平移  5*pi/3=300度\n",
    "new_dino = translate((8,8),[rotate1(5*pi/3,p) for p in dino_vectors])\n",
    "# 先平移再旋转\n",
    "tra = translate((8,8),dino_vectors)\n",
    "new_dino2 = [rotate1(5*pi/3 , v) for v in tra]\n",
    "draw(\n",
    "    Polygon(*new_dino, color=blue),\n",
    "    Polygon(*dino_vectors, color=gray),\n",
    "    Polygon(*new_dino2, color=red),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "from matplotlib.patches import Polygon\n",
    "from matplotlib.collections import PatchCollection"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
